```Date: Jan 31, 2013 3:23 AM
Author: William Elliot
Subject: Re: Beating the Odds?

On Wed, 30 Jan 2013, forbisgaryg@gmail.com wrote:> On Wednesday, January 30, 2013 12:29:09 AM UTC-8, William Elliot wrote:> > There is a fair coin with a different integer on each side that you can't > > see and you have no clue how these integers were selected. The coin is > > flipped and you get to see what comes up. You must guess if that was the > > larger of the two numbers or not. Can you do so with probability > 1/2?> > Well, there was the monty hall problem years ago.  Suppose there are 3 > keys and you have to choose one.  One of the three turns on a car's engine> where the other two do not.  After you choose a key Monte takes one and> tries it in the car and it doesn't turn over the engine.  He then asks> you if you'd like to change your mind.  What should you do?  You should > change your mind because the first key you chose had a one in three chance> of turning on the car where the remaining key has a two in three chance.> > Soo...> > Assuming the coin only has positive integers then you should guess> the number showing is the smaller integer because there are more> integers greater than x than there are less than x and this is true> for all positive integers x.> Recall, you have no clue how the integers were selected much less that both are positive or non-negative.Here's a variant.  Instead of integers, the coin has a positive rational on each side.
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